The home secretary, Theresa May, has refused to set a minimum turnout for next week's police and crime commissioner elections, in the face of claims that it could fall to the lowest in British election history.

May said the new commissioners holding the police to account across England and Wales would have a democratic mandate even if the turnout fell to 10% or 15%, and would be more "visible and accessible" than the police authorities they are to replace.

The home secretary said the latest polling data showed that 62% of people were aware the elections were happening on 15 November.

May also told the BBC's Today programme that the commissioners would not be able to interfere with the operational independence of the police, who would be able to carry out investigations and arrests "without fear or favour" after next week's elections.

The Electoral Reform Society has warned that the turnout for the £75m policing elections could fall to as little as 18% – the lowest in British polling history – leaving a question mark against the legitimacy of the elected commissioners. One recent Ipsos Mori poll suggested turnout could even fall to 15%.

The elections are being held in the 41 police force areas across England and Wales outside London.

When the home secretary was asked how a 15% turnout could amount to a democratic mandate, she said she was not going to set a minimum threshold for turnout. She said: "I never set a turnout threshold for any election and I'm not going to do it now. The people elected as police commissioners will have something that the current police authorities do not have, which is a democratic mandate.

"The point is that these are the first elections for police and crime commissioners. For the first time ever an individual who is responsible for setting police budgets and strategic priorities will be elected."

May added that only 7% of people had even heard of the police authorities that the commissioners would replace. She said the commissioners should not be judged on the turnout in their individual election but on their ability to set priorities for the police and to cut crime.

The home secretary said Boris Johnson's role as mayor of London overseeing the Metropolitan police was a model for how the new policing commissioners would work outside London. Johnson notably sacked Sir Ian Blair as Met chief, and the new commissioners will also have the power to hire and fire chief constables.

May said a police and crime panel sitting alongside the elected commissioner would make sure their decisions, including the sacking of a chief constable, were not taken "maliciously or capriciously". She cited Johnson's decision to put more police officers on late-night London buses as an example of what a commissioner could do without interfering in the operational independence of the police.

The government's decision to sweep away all Whitehall targets for the police meant the commissioners could also play a key role in ensuring a local voice was heard in decisions on resources and priorities.

Last week Labour's Lord Prescott, who is standing for the police commissioner job in Humberside, warned that November was the worst time to hold an election. He said no money was being given for the election candidates and little information provided to the public about them. He warned that a low turnout would call into question the legitimacy of commissioners.

The Guardian Northerner is keen to add to interest in the coming elections on Thursday 15 November. Here, regular contributor Janice Gwilliam shows how those who reject the whole idea can still take part